1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Relativistic Group Velocity Calculation

  1. Oct 29, 2007 #1
    1. The problem statement, all variables and given/known data

    we are given that an electron and a proton have the same KE.We are to compare their phase and group velocity...

    2. Relevant equations

    3. The attempt at a solution

    Now, I found it very problematic to extract the ratio of v₁/v₂ in terms of m₁ and m₂
    So,I expanded the γ s binomially where the major contribution comes from the first few terms...It follows that group velocity if proton is much less than that of the electron...

    Please tell me if I am correct and sggest any other possible ways...

  2. jcsd
  3. Oct 29, 2007 #2


    User Avatar
    Science Advisor

    Don't use v.
    Use E=T+M and p=\sqrt{T^2+2M}.
  4. Oct 29, 2007 #3
    but how would you compae between the group velocities???

    I hope your formula is pc=√[K(K+2mc²)] where K is the KE

    But, p=γmv...so that you are to know γ if you want to know v
    γ s are different for e and p...
  5. Oct 29, 2007 #4


    User Avatar
    Science Advisor

    Sorry, I should have had T=\sqrt{T^2+2MT}.
    I use T for KE, which is more common, and relativistic units with c absent.
    v_P=E/p, and v_g=dE/dp=p/E.
    You don't need gamma or v, but they are gamma=E/M and v=p/E.
  6. Oct 29, 2007 #5
    Buddy,what you are using seems not quite effective here...Remember we are to compare between group and phase velocities of an e and a p whose KE are the same...And you have not used the fact that their KE are the same...

    I am referring to another method...It is no approximation..stands on sheer logic...

    1 stands for e and 2 stands for p



    => γ₂<γ₁
    From which you can deduce the relation between group and phase velocity...
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Relativistic Group Velocity Calculation
  1. Group Velocity (Replies: 1)